A bucket tappet of said type can be gathered from DE 44 92 633 C1, which is regarded as being generic. The coupling mechanism of the bucket tappet is arranged directly below the base. A person skilled in the art will recognize that the already known tappet is of relatively complex design, and the production thereof has therefore proven to be unnecessarily expensive. For example, the outer part is of asymmetrical design in the base region, since guide bores for the coupling piston are formed directly below the annular base. It can also be seen that the inner part is of unnecessarily massive design, in particular in the base region. Said massive design is associated with an undesired increase in the oscillating valve drive masses. Furthermore, on account of the piston-in-bore coupling, a relatively high component loading can occur in the coupling section, and anti-twist measures are necessary between the bucket basic body and the inner body.